name string | module string | deps list | allowCompletion bool |
|---|---|---|---|
Quiver.Path.nil | Mathlib.Combinatorics.Quiver.Path | [
"Quiver.Path.nil",
"Quiver.Path",
"Quiver"
] | true |
SpecialLinearGroup.coe_div | Mathlib.LinearAlgebra.SpecialLinearGroup | [
"LinearEquiv.det",
"CommRing",
"MonoidHom.instFunLike",
"instHDiv",
"MonoidHom",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"SpecialLinearGroup",
"Units",
"AddCommGroup",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"Units.instOne",
"Group.toDivInvMonoid"... | true |
MeasurableSpace.exists_eq_iUnion_countablyGeneratedAtom | Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated | [
"Mathlib.Tactic.Push.not_forall_eq",
"Set.ext",
"Eq.mpr",
"False",
"MeasurableSet",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"iSup",
"Set.iInter",
"Mathlib.Tactic.Contrapose.contrapose₃",
"Compl.compl",
"Set.mem_iUnion._simp_1",
"Classical.propDecidable",
"_private.Ma... | true |
Lean.Parser.Tactic.MCasesPat | Std.Tactic.Do.Syntax | [
"Lean.Parser.Tactic.MCasesPat.alts",
"Lean.Parser.Tactic.MCasesPat.one",
"Lean.Parser.Tactic.MCasesPat.stateful",
"Lean.Parser.Tactic.MCasesPat.pure",
"Lean.Parser.Tactic.MCasesPat.clear",
"Lean.Parser.Tactic.MCasesPat.tuple"
] | true |
RingCat.ringObj._proof_46 | Mathlib.Algebra.Category.Ring.Limits | [
"RingCat.ringObj._proof_22",
"AddGroupWithOne.intCast_negSucc._autoParam",
"Semiring.toNatCast",
"RingCat.ringObj._proof_19",
"RingCat.ringObj._proof_27",
"CategoryTheory.Functor",
"RingCat.ringObj._aux_4",
"RingCat.ringObj._proof_3",
"RingCat.ringObj._proof_15",
"RingCat.ringObj._aux_13",
"Ring... | false |
_private.Init.Data.List.Impl.0.List.zipWith_eq_zipWithTR.go | Init.Data.List.Impl | [
"List.brecOn",
"List.zipWith",
"Array.toList",
"Array",
"instHAppendOfAppend",
"List",
"_private.Init.Data.List.Impl.0.List.zipWith_eq_zipWithTR.go._f",
"List.instAppend",
"Eq",
"_private.Init.Data.List.Impl.0.List.zipWithTR.go",
"HAppend.hAppend"
] | true |
NonUnitalSubsemiring.inclusion._proof_1 | Mathlib.RingTheory.NonUnitalSubsemiring.Defs | [
"Membership.mem",
"Subtype",
"NonUnitalSubsemiring.instNonUnitalSubsemiringClass",
"NonUnitalRingHom.instFunLike",
"NonUnitalRingHom.instNonUnitalRingHomClass",
"NonUnitalSubsemiring.instSetLike",
"NonUnitalSubsemiring",
"NonUnitalRingHomClass",
"NonUnitalSubsemiringClass.toNonUnitalNonAssocSemiring... | false |
_private.Lean.Elab.Match.0.Lean.Elab.Term.elabMatchTypeAndDiscrs.elabDiscrs._unsafe_rec | Lean.Elab.Match | [
"Pure.pure",
"Lean.instantiateMVars",
"Unit.unit",
"Lean.instMonadMCtxOfMonadLift",
"Lean.Elab.Term.Discr",
"Array.push",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Elab.Term.ElabMatchTypeAndDiscrsResult.alts",
"ReaderT",
"instMonadControlTOfPure",
"Monad.toApplicative",
"Lean.Meta.State",
"... | false |
WeierstrassCurve.Projective.Point.mk.inj | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point | [
"WeierstrassCurve.Projective.Point",
"CommRing",
"WeierstrassCurve.Projective.Point.mk",
"WeierstrassCurve.Projective.Point.mk.noConfusion",
"WeierstrassCurve.Projective",
"eq_of_heq",
"HEq",
"WeierstrassCurve.Projective.PointClass",
"Eq",
"WeierstrassCurve.Projective.NonsingularLift"
] | true |
LinearMap.IsIdempotentElem.isSymmetric_iff_isOrtho_range_ker | Mathlib.Analysis.InnerProductSpace.Symmetric | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"RingHomSurjective.ids",
"Submodule.projection",
"NormedRing.toRing",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Iff.rfl",
"LinearMap.ker",
"LinearMap.IsProj.isCompl",
"Module.End.instMul",
... | true |
Std.TreeMap.Raw.equiv_iff_keys_unit_perm | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.keys",
"Std.DTreeMap.Raw.Const.equiv_iff_keys_unit_perm",
"Ordering",
"Std.DTreeMap.Raw.Equiv",
"List.Perm",
"Std.TreeMap.Raw.Equiv",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Unit",
"Iff",
"_private.Std.Data.TreeMap.Raw.Lemmas.0.Std.TreeMap.Raw.equiv_iff",
"Iff.trans"
] | true |
dist_le_range_sum_dist | Mathlib.Topology.MetricSpace.Pseudo.Basic | [
"Nat.zero_le",
"Real.instLE",
"Real",
"Finset",
"Nat.instLocallyFiniteOrder",
"Eq.rec",
"Finset.Ico",
"instOfNatNat",
"LE.le",
"Finset.range",
"instHAdd",
"PseudoMetricSpace",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"Nat.Ico_zero_eq_range",
"Real.instAddCommMonoid",
"instAddNat",
... | true |
Array.forM_append | Init.Data.Array.Monadic | [
"Array.instAppend",
"ForM.forM",
"congrArg",
"List.forM_append",
"Array.instForMOfMonad",
"Array.casesOn",
"LawfulMonad",
"List.append_toArray",
"List.forM_toArray",
"List.toArray",
"Array",
"funext",
"instHAppendOfAppend",
"List",
"PUnit",
"congr",
"True",
"eq_self",
"of_eq_true... | true |
CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor._proof_2 | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.ComposableArrows.homMk₅",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.SnakeInput.naturality_δ",
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._proof_455",
"instNeZeroNatHAdd_1",
"CategoryTheory.ShortComplex.SnakeInput.L₃",
"CategoryTheory.CategoryStru... | false |
Mathlib.Meta.FunProp.LambdaTheorems._sizeOf_inst | Mathlib.Tactic.FunProp.Theorems | [
"Mathlib.Meta.FunProp.LambdaTheorems._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Mathlib.Meta.FunProp.LambdaTheorems"
] | false |
CStarMatrix.ofMatrixRingEquiv._proof_2 | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"Matrix.add",
"Matrix",
"Distrib.toAdd",
"Equiv.toFun",
"instDistribOfSemiring",
"CStarMatrix.ofMatrix",
"CStarMatrix",
"instHAdd",
"HAdd.hAdd",
"Semiring",
"Eq",
"rfl"
] | false |
Ordinal.max_zero_right | Mathlib.SetTheory.Ordinal.Basic | [
"Ordinal.instLinearOrder",
"Lattice.toSemilatticeSup",
"instIsBotZeroClass",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice... | true |
_private.Mathlib.Order.Interval.Set.LinearOrder.0.Set.Ioc_inter_Ioc._proof_1_1 | Mathlib.Order.Interval.Set.LinearOrder | [
"instLawfulOrderLT_mathlib",
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"Set.ext",
"Set.Ioc",
"of_eq_false",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",... | false |
Algebra.IsPushout.symm | Mathlib.RingTheory.IsTensorProduct | [
"AlgHom.toLinearMap",
"AlgEquiv.instEquivLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Algebra.to_smulCommClass",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"IsScalarTower.right",
"Equiv.right_inv",
"LinearEquiv.mk",
"Algebra.algebraMap",
"NonUnitalAlgHom... | true |
Interval._aux_Mathlib_Order_Interval_Set_UnorderedInterval___macroRules_Interval_termΙ_1 | Mathlib.Order.Interval.Set.UnorderedInterval | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad",
"Lean.TSyntax.... | false |
PiTensorProduct.mapMultilinear_apply | Mathlib.LinearAlgebra.PiTensorProduct | [
"PiTensorProduct.instModule",
"PiTensorProduct.map",
"PiTensorProduct.mapMultilinear",
"CommSemiring.toSemiring",
"PiTensorProduct.instSMulCommClass",
"PiTensorProduct.instAddCommMonoid",
"LinearMap.module",
"LinearMap",
"MultilinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
... | true |
«term_=_» | Init.Notation | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc | Mathlib.CategoryTheory.Limits.Constructions.Over.Products | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Over",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.prod.fst",
"CategoryTheory.Over.Hom.left",
"Eq.mp",
"id",
"CategoryTheory.Limits.HasPullback",
"Mathlib.Tactic.Re... | true |
_private.Init.Data.List.Perm.0.List.reverse_perm.match_1_1 | Init.Data.List.Perm | [
"Unit.unit",
"List.cons",
"List",
"Unit",
"List.casesOn",
"List.nil"
] | false |
Matrix.det_of_mem_unitary | Mathlib.LinearAlgebra.UnitaryGroup | [
"MulOne.toOne",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"unitary",
"AddGroupWithOne.toAddMonoidWithOne",
... | true |
Std.DTreeMap.Internal.Impl.Const.getThenInsertIfNew? | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"Std.DTreeMap.Internal.Impl.Const.getThenInsertIfNew?.match_1",
"Std.DTreeMap.Internal.Impl.Balanced",
"Option.some",
"Std.DTreeMap.Internal.Impl.size",
"Prod.mk",
"instOfNatNat",
"Option.none",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat... | true |
instAB4AddCommGrpCat | Mathlib.Algebra.Category.Grp.AB | [
"AddCommGrpCat.instCategory",
"AddCommGrpCat.hasLimits",
"instHasFilteredColimitsAddCommGrpCat",
"AddCommGrpCat.instHasFiniteBiproducts",
"UnivLE.small",
"CategoryTheory.Limits.hasCountableLimits_of_hasLimits",
"CategoryTheory.instSmallDiscrete",
"CategoryTheory.discreteCategory",
"UnivLE.self",
"... | true |
CategoryTheory.ObjectProperty.homMk_surjective | Mathlib.CategoryTheory.ObjectProperty.FullSubcategory | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.ObjectProperty.homMk",
"Exists.intro",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.InducedCategory.Hom.hom",
"CategoryTheory.ObjectProperty.FullSubcategory",
"... | true |
ContinuousAt.lineMap | Mathlib.Topology.Algebra.Affine | [
"Semiring.toModule",
"AffineMap.instFunLike",
"ContinuousSMul",
"AddGroupWithOne.toAddGroup",
"ContinuousAt",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsTopologicalAddTorsor",
"AddMonoid.toAddZeroClass",
"AffineMap.lineMap",
"instTopologicalSpaceProd",
"AddCommGroup.t... | true |
Lean.CollectMVars.State.result | Lean.Util.CollectMVars | [
"Lean.MVarId",
"Array",
"Lean.CollectMVars.State"
] | true |
Module.Basis.constrL._proof_1 | Mathlib.Topology.Algebra.Module.FiniteDimension | [
"AddCommGroup.toAddCommMonoid",
"Finite",
"NormedDivisionRing.toDivisionRing",
"NormedField.toField",
"AddCommGroup",
"NormedField.toNormedDivisionRing",
"Field.toSemifield",
"Module.Basis.finiteDimensional_of_finite",
"Module.Basis",
"FiniteDimensional",
"Semifield.toDivisionSemiring",
"Divis... | false |
AddMonoidAlgebra.le_infDegree_mul | Mathlib.Algebra.MonoidAlgebra.Degree | [
"Eq.ge",
"HMul.hMul",
"AddHom",
"AddMonoidAlgebra.infDegree",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"AddHom.addHomClass",
"SemilatticeInf.toPartialOrder",
"AddRightMono",
"AddZeroClass.toAddZero",
"map_add",
"LE.le",
"AddHom.funLike",
"OrderTop",
"AddMonoidAlgebra.... | true |
Lean.Elab.Term.Quotation.elabQuot._@.Lean.Elab.Quotation.1964439861._hygCtx._hyg.3 | Lean.Elab.Quotation | [
"Lean.Elab.Term.TermElab",
"Lean.Elab.Term.adaptExpander",
"Lean.Elab.Term.Quotation.stxQuot.expand"
] | false |
Substring.Raw.str | Init.Prelude | [
"String",
"Substring.Raw"
] | true |
_private.Mathlib.RingTheory.Polynomial.UniversalFactorizationRing.0.Polynomial.instFiniteUniversalFactorizationRing._proof_1 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"Polynomial.MonicDegreeEq",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"AlgHom",
"TensorProduct.addCommMonoid",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",... | false |
_private.Mathlib.Data.Int.Interval.0.Int.instLocallyFiniteOrder._proof_5 | Mathlib.Data.Int.Interval | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"HMul.hMul",
"Int.Linear.norm_le",
"Lean.Grind.not_and",
"eq_false",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Int.Linear.eq_norm",
"Classical.b... | false |
DirectLimit.instCommGroupWithZeroOfMonoidWithZeroHomClass._proof_7 | Mathlib.Algebra.Colimit.DirectLimit | [
"GroupWithZero.toMonoidWithZero",
"GroupWithZero.zpow",
"Semigroup.toMul",
"HMul.hMul",
"GroupWithZero",
"Preorder.toLE",
"inferInstance",
"Int",
"LE.le",
"Nat.cast",
"DirectLimit",
"MonoidWithZeroHomClass",
"DirectLimit.instGroupWithZero",
"MonoidWithZero.toMulZeroOneClass",
"Nat",
"I... | false |
instCompleteLatticeStructureGroupoid._proof_7 | Mathlib.Geometry.Manifold.StructureGroupoid | [
"Lattice.toSemilatticeSup",
"completeLatticeOfInf",
"CompleteLattice.toLattice",
"StructureGroupoid.partialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"StructureGroupoid",
"instCompleteLatticeStructureGroupoid._proof_1",
"LE.le",
"TopologicalSpace",
"instInfSetStructureGroupoid",
"Semi... | false |
_private.Mathlib.RingTheory.Nilpotent.Exp.0.IsNilpotent.exp_add_of_commute._proof_1_3 | Mathlib.RingTheory.Nilpotent.Exp | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Classical.byContradiction",
"Nat.not_le_eq",
"Nat.Linear.Expr.mulL",
"id",
"False.casesOn",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Linear.Expr.num",
"Bool.true",
"instHAdd",
"Nat.Linear.ExprCnstr.eq_false_of_isUnsat",
"HAdd... | false |
Lean.Meta.NormCast.normCastExt | Lean.Meta.Tactic.NormCast | [
"Inhabited.default",
"Lean.Meta.NormCast.NormCastExtension",
"Lean.Meta.NormCast.instInhabitedNormCastExtension"
] | true |
_private.Lean.Meta.Tactic.ExposeNames.0.Lean.Meta.getLCtxWithExposedNames | Lean.Meta.Tactic.ExposeNames | [
"Pure.pure",
"Unit.unit",
"Lean.Meta.isProp",
"Bool.not",
"Std.HashMap.contains",
"Lean.Meta.instMonadLCtxMetaM",
"Array.push",
"instForInOfForIn'",
"Lean.Meta.State",
"HSub.hSub",
"Option.getD",
"Array.instMembership",
"Lean.instForInLoopUnitOfMonad",
"Membership.mem",
"Lean.LocalDecl.i... | true |
List.cons.inj | Init.Core | [
"List.cons",
"List",
"And",
"And.intro",
"eq_of_heq",
"HEq",
"Eq",
"List.cons.noConfusion"
] | true |
Empty.borelSpace | Mathlib.MeasureTheory.Constructions.BorelSpace.Basic | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Empty.instMeasurableSpace",
"Preorder.toLE",
"borel_eq_top_of_discrete",
"BorelSpace",
"CompleteLattice.toBoundedOrder",
"borel",
"MeasurableSpace",
"Empty",
"OrderTop.toTop",
"BoundedOrder.toOrderTop",
"B... | true |
TopCat.isoOfHomeo._proof_1 | Mathlib.Topology.Category.TopCat.Basic | [
"ContinuousMapClass",
"TopCat.str",
"Homeomorph.instEquivLike",
"TopCat.carrier",
"Homeomorph",
"TopCat",
"Homeomorph.instContinuousMapClass",
"EquivLike.toFunLike"
] | false |
LocallyFinite.exists_finset_support | Mathlib.Topology.Algebra.Monoid | [
"Filter.instMembership",
"Eq.mpr",
"congrArg",
"Finset",
"Filter.Eventually",
"setOf",
"Set.Finite",
"Membership.mem",
"Exists",
"nhds",
"id",
"Set.Finite.coe_toFinset",
"HasSubset.Subset",
"Set.instInter",
"LocallyFinite",
"Inter.inter",
"And.casesOn",
"TopologicalSpace",
"And",... | true |
QuaternionAlgebra.Basis.k_compHom | Mathlib.Algebra.QuaternionBasis | [
"CommRing",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"QuaternionAlgebra.Basis.k",
"QuaternionAlgebra.Basis.compHom",
"CommRing.toCommSemiring",
"Eq.refl",
"QuaternionAlgebra.Basis",
"Ring.toSemiring",
"Eq",
"DFunLike.coe",
"Ring"
] | true |
Equiv.completeAtomicBooleanAlgebra._proof_6 | Mathlib.Order.CompleteBooleanAlgebra | [
"Equiv.apply_symm_apply",
"iInf",
"Equiv.instEquivLike",
"CompleteAtomicBooleanAlgebra",
"Membership.mem",
"Equiv",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteBooleanAlgebra.toCompleteLattice",
"CompleteSemilatticeInf.toInfSet",
"Equiv.symm",
"Eq",
"Set.instMembership",
"DFunLike.c... | false |
_private.Lean.Server.Completion.CompletionInfoSelection.0.Lean.Server.Completion.findCompletionInfosAt.go.match_3 | Lean.Server.Completion.CompletionInfoSelection | [
"Lean.Elab.CompletionInfo",
"Nat.hasNotBit",
"Lean.Elab.Info.ofCompletionInfo",
"_private.Lean.Server.Completion.CompletionInfoSelection.0.Lean.Server.Completion.findCompletionInfosAt.go._sparseCasesOn_3",
"Lean.Elab.Info.ctorIdx",
"Lean.Elab.Info"
] | false |
CategoryTheory.Limits.image.compIso._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.IsIso",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.mono_of_strongMono",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.strongMono_of_isIso",
"CategoryTheory.Category"
] | false |
Mathlib.Tactic.ToDual.data | Mathlib.Tactic.Translate.ToDual | [
"Mathlib.Tactic.ToDual.doTranslateAttr",
"Mathlib.Tactic.Translate.TranslateData.mk",
"Mathlib.Tactic.ToDual.ignoreArgsAttr",
"Option.some",
"Mathlib.Tactic.ToDual.guessNameExt",
"Bool.true",
"Mathlib.Tactic.Translate.TranslateData",
"Mathlib.Tactic.ToDual.unfoldBoundaries",
"Mathlib.Tactic.ToDual.t... | true |
Std.Tactic.BVDecide.BVExpr.bitblast.goCache._mutual._proof_53 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Expr | [
"Std.Sat.AIG.Decl",
"Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorRefVecBlastCpop",
"LE.le",
"instLENat",
"Subtype.mk",
"Std.Sat.AIG",
"Nat",
"Std.Sat.AIG.RefVecEntry.mk",
"Std.Tactic.BVDecide.instDecidableEqBVBit",
"Std.Sat.AIG.RefVecEntry.aig",
"Std.Sat.AIG.RefVecEntry",
"Std.Sat... | false |
Std.Time.Month.Ordinal.january | Std.Time.Date.Unit.Month | [
"OfNat.ofNat",
"Std.Time.Month.Ordinal",
"Std.Time.Month.instOfNatOrdinal"
] | true |
_private.Lean.PrettyPrinter.Delaborator.TopDownAnalyze.0.Lean.PrettyPrinter.Delaborator.TopDownAnalyze.containsBadMax._sparseCasesOn_1 | Lean.PrettyPrinter.Delaborator.TopDownAnalyze | [
"Lean.Level.ctorIdx",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Level.mvar",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level.imax",
"instOfNatNat",
"Lean.Level",
"Nat.land",
"Lean.Level.zero",
"Nat",
"Bool",
"Lean.Level.rec",
"Lean.Name",
"Eq.refl",
"Lean.Level.succ",
"OfN... | false |
_private.Mathlib.Analysis.Fourier.ZMod.0.ZMod.auxDFT_smul | Mathlib.Analysis.Fourier.ZMod | [
"NegZeroClass.toNeg",
"Nat.instMulZeroClass",
"instHSMul",
"HMul.hMul",
"Finset.univ",
"ZMod.commRing",
"Complex.commRing",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Finset",
"ZMod.stdAddChar",
"SMul",
"ZMod.fintype",
"Add... | true |
cantorToTernary_ne_one | Mathlib.Topology.Instances.CantorSet | [
"Real",
"cantorToTernary",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"_private.Mathlib.Topology.Instances.CantorSet.0.cantorToTernary_ne_one._proof_1_2",
"Stream'.get",
"Nat.instNeZeroSucc",
"Nat",
"OfNat.ofNat",
"Fin"
] | true |
CategoryTheory.Tor._proof_4 | Mathlib.CategoryTheory.Monoidal.Tor | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.MonoidalPreadditive",
"CategoryTheory.MonoidalCategory.tensoringLeft",
"Catego... | false |
_private.Init.Data.String.Lemmas.Pattern.Basic.0.String.Slice.Pattern.Model.isRevMatch_sliceFrom_iff._simp_1_1 | Init.Data.String.Lemmas.Pattern.Basic | [
"String.Slice.Pattern.Model.IsRevMatch",
"String.Slice.Pattern.Model.PatternModel.Matches",
"String.Slice.sliceFrom",
"String.Slice",
"String.Slice.copy",
"propext",
"String.Slice.Pattern.Model.isRevMatch_iff",
"String.Slice.Pattern.Model.PatternModel",
"String.Slice.Pos",
"Eq"
] | false |
CommAlgCat.inv_hom_apply | Mathlib.Algebra.Category.CommAlgCat.Basic | [
"CommAlgCat.instConcreteCategoryAlgHomCarrier",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"AlgHom",
"AlgHom.funLike",
"CommAlgCat.commRing",
"CategoryTheory.Iso",
"CommAlgCat.instCategory",
"CategoryTheory.Iso.hom_inv_id_apply",
"CommAlgCat.carri... | true |
CategoryTheory.SimplicialObject.Homotopy.mk._flat_ctor | Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Fin.succ",
"CategoryTheory.SimplicialObject.Homotopy.mk",
"CategoryTheory.Functor.category",
"instOfNatNat",
"LE.le",
"instLEFin",
"CategoryTheory.SimplicialObject.Homotopy",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
... | false |
Lean.AssocList.nil.elim | Lean.Data.AssocList | [
"Lean.AssocList.nil",
"PULift.up",
"Lean.AssocList.ctorElim",
"Lean.AssocList.ctorIdx",
"Nat",
"Lean.AssocList",
"Eq.symm",
"Eq"
] | false |
Aesop.RuleResult.ctorIdx | Aesop.Search.Expansion | [
"Aesop.RappRef",
"Array",
"Aesop.RuleResult.casesOn",
"Nat",
"Aesop.RuleResult"
] | false |
Std.Tactic.BVDecide.BVExpr.bitblast.blastAdd._proof_4 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Add | [
"_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Add.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastAdd._proof_3",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Not",
"... | false |
clusterPt_principal_subtype_iff_frequently | Mathlib.Topology.NhdsWithin | [
"Subtype.coe_mk",
"Iff.mpr",
"Eq.mpr",
"Topology.IsInducing.nhds_eq_comap",
"_private.Mathlib.Topology.NhdsWithin.0.clusterPt_principal_subtype_iff_frequently._simp_1_3",
"_private.Mathlib.Topology.NhdsWithin.0.clusterPt_principal_subtype_iff_frequently.match_1_4",
"Iff.of_eq",
"congrArg",
"Filter.m... | true |
_private.Mathlib.Tactic.Ring.Common.0.Mathlib.Tactic.Ring.Common.eval.match_17 | Mathlib.Tactic.Ring.Common | [
"Mathlib.Tactic.Ring.Common.Result.mk",
"Lean.Expr.const",
"Mathlib.Tactic.Ring.Common.Result",
"Mathlib.Tactic.Ring.Common.ExSum",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Mathlib.Tactic.Ring.Common.Result.casesOn",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
... | false |
CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'._proof_4 | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData.f'",
"CategoryTheory.IsIso",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct... | false |
Graph.inf_inc_iff._simp_1 | Mathlib.Combinatorics.Graph.Lattice | [
"Graph.inf_inc_iff",
"Graph.Inc",
"Exists",
"Graph.instSemilatticeInf",
"Graph",
"SemilatticeInf.toMin",
"And",
"Graph.IsLink",
"propext",
"Eq",
"Min.min"
] | false |
LinearMap.tensorEqLocusInv._proof_2 | Mathlib.RingTheory.Flat.Equalizer | [
"Submodule",
"CommRing",
"Module.Flat.lTensor_preserves_injective_linearMap",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"TensorProduct.addCommMonoid",
"LinearMap.instFunLike",
"Membership.mem",
"LinearMap.lTensor",
"AddCommGroup",
"Subtype",
"Submo... | false |
MeasureTheory.laverage_mul_measure_univ | Mathlib.MeasureTheory.Integral.Average | [
"Iff.mpr",
"Eq.mpr",
"MeasureTheory.Measure",
"instHDiv",
"HMul.hMul",
"MeasureTheory.laverage",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"MeasureTheory.laverage_zero_measure",
"MeasureTheory.Measure.measure_univ_ne_zero",
"MeasureTheory.measure_ne_top",
"MeasureTheory.laverage_eq"... | true |
Std.DTreeMap.Internal.Impl.Const.get!ₘ | Std.Data.DTreeMap.Internal.Model | [
"Ord",
"Option.get!",
"Inhabited",
"Std.DTreeMap.Internal.Impl.Const.get?ₘ",
"Std.DTreeMap.Internal.Impl"
] | true |
String.skipPrefix? | Init.Data.String.TakeDrop | [
"String.toSlice",
"String",
"String.Slice.skipPrefix?",
"String.Slice.Pattern.ForwardPattern",
"Option.map",
"String.Pos.ofToSlice",
"String.Pos",
"String.Slice.Pos",
"Option"
] | true |
_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1.stmts₁_supportsStmt_mono._simp_1_15 | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Finset.instUnion",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"propext",
"Finset.mem_union",
"Or",
"Union.union",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
Subsemiring.instTop._proof_2 | Mathlib.Algebra.Ring.Subsemiring.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddSubmonoid.instTop",
"AddMonoid.toAddZeroClass",
"AddSubsemigroup.carrier",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"AddSubmonoid",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddZero.toZero",
"NonAssocSemiring",... | false |
Ideal.span_singleton_absNorm_le | Mathlib.RingTheory.Ideal.Norm.AbsNorm | [
"Nat.instMulZeroOneClass",
"CommRing",
"Semiring.toModule",
"Ideal.absNorm",
"CommSemiring.toSemiring",
"Ideal.absNorm_mem",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"MonoidWithZeroHom.funLike",
"Preorder.toLE",
"Membership.mem",
"Algebra.id",
"Set.instSingletonSet",
... | true |
_private.Mathlib.RepresentationTheory.Induced.0.Rep.indResHomEquiv._simp_1 | Mathlib.RepresentationTheory.Induced | [
"Representation.Coinvariants.mk_inv_tmul",
"CommRing",
"Representation",
"MonoidHom.instFunLike",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Module.End.instSemiring",
"LinearMap.instFunLike",
"Group",
"Group.toDivisionMo... | false |
_private.Lean.Meta.Tactic.Simp.Simproc.0.Lean.Meta.Simp.initFn._@.Lean.Meta.Tactic.Simp.Simproc.1481072680._hygCtx._hyg.2 | Lean.Meta.Tactic.Simp.Simproc | [
"Lean.Meta.SimpTheoremKey",
"IO.mkRef",
"instMonadLiftT",
"IO",
"Sum",
"EIO",
"liftM",
"Std.HashMap",
"Std.HashMap.instEmptyCollection",
"Array",
"Lean.Meta.Simp.DSimproc",
"Lean.Name",
"IO.Error",
"IO.Ref",
"instMonadLiftTOfMonadLift",
"EmptyCollection.emptyCollection",
"BaseIO",
... | false |
NormalizationMonoid.ofUniqueUnits | Mathlib.Algebra.GCDMonoid.Basic | [
"NormalizationMonoid",
"Units",
"NormalizationMonoid.ofUniqueUnits._proof_2",
"CommMonoidWithZero.toMonoidWithZero",
"Units.instOne",
"NormalizationMonoid.ofUniqueUnits._proof_1",
"CommMonoidWithZero",
"NormalizationMonoid.mk",
"One.toOfNat1",
"Subsingleton",
"OfNat.ofNat",
"MonoidWithZero.toM... | true |
MonoidHom.toAdditiveRightMulEquiv._proof_1 | Mathlib.Algebra.Group.TypeTags.Hom | [
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"Equiv.trans",
"Additive",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Multiplicative.mulOneClass",
"Additive.addZeroClass",
"Equiv.toFun",
"Multiplicative",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"AddMonoid",
"Multipli... | false |
_private.Mathlib.Algebra.Module.Submodule.Lattice.0.Submodule.mem_finsetInf._simp_1_2 | Mathlib.Algebra.Module.Submodule.Lattice | [
"Set.iInter",
"Membership.mem",
"Set.mem_iInter",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
QuadraticAlgebra.coe_injective | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"QuadraticAlgebra",
"QuadraticAlgebra.C",
"QuadraticAlgebra.C_injective",
"Function.Injective",
"Zero"
] | true |
Matroid.IsStrictMinor.trans | Mathlib.Combinatorics.Matroid.Minor.Order | [
"Matroid.instPartialOrder",
"PartialOrder.toPreorder",
"Matroid.IsStrictMinor",
"LT.lt.trans",
"Matroid.IsStrictMinor.lt",
"Matroid"
] | true |
RootPairing.Hom.comp._proof_3 | Mathlib.LinearAlgebra.RootSystem.Hom | [
"Eq.mpr",
"RootPairing.Hom.indexEquiv",
"CommRing",
"Equiv.instEquivLike",
"congrArg",
"CommSemiring.toSemiring",
"Equiv.trans",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"Function.comp",
"AddCommGroup",
"id",
"Equiv",
"RootPairing.Hom.coroot_coweightMap",
"LinearMap",
"... | false |
Polynomial.associated_of_dvd_of_natDegree_le_of_leadingCoeff | Mathlib.Algebra.Polynomial.Div | [
"Units.val",
"Eq.mpr",
"Polynomial.C",
"IsDomain",
"False",
"Semigroup.toMul",
"CommRing",
"IsDomain.to_noZeroDivisors",
"Dvd.dvd",
"MonoidHom.instFunLike",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Polynomial.leadingCoeff_mul",
"MonoidHom",
"MulZeroClass.toMul",
"Monoid.toMulOneCl... | true |
Lean.Grind.CommRing.Poly | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly.add",
"Lean.Grind.CommRing.Poly.num"
] | true |
TrivSqZeroExt.addMonoid._proof_1 | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"TrivSqZeroExt",
"AddMonoid.toAddSemigroup",
"TrivSqZeroExt.addSemigroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Prod.instAddMonoid._proof_1",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"AddMonoid",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"TrivSqZeroE... | false |
SchwartzMap.compCLM._proof_3 | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | [
"NormedCommRing.toSeminormedCommRing",
"SeminormedRing.toNorm",
"SeminormedRing.toRing",
"RingHomIsometric",
"RingHomIsometric.ids",
"RCLike.toDenselyNormedField",
"RCLike",
"SeminormedCommRing.toSeminormedRing",
"NormedField.toNormedCommRing",
"DenselyNormedField.toNormedField",
"RingHom.id",
... | false |
CategoryTheory.MorphismProperty.precoverage_monotone | Mathlib.CategoryTheory.Sites.MorphismProperty | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Precoverage",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.Precoverage.instPartialOrder",
"CategoryTheory.Presieve",
"PartialOrder.toPreorder",
"Preorder.toLE",... | true |
ContinuousWithinAt.eq_const_of_mem_closure | Mathlib.Topology.Separation.Basic | [
"Eq.mpr",
"ContinuousWithinAt.mem_closure",
"ContinuousWithinAt",
"congrArg",
"Membership.mem",
"Set.instSingletonSet",
"id",
"closure_singleton",
"TopologicalSpace",
"Set.mem_singleton_iff",
"closure",
"propext",
"T1Space",
"Singleton.singleton",
"Eq.symm",
"Eq",
"Set.instMembership... | true |
MeasureTheory.OuterMeasure.trim_zero | Mathlib.MeasureTheory.OuterMeasure.Induced | [
"ENNReal.instCanonicallyOrderedAdd",
"LE.le.trans_eq",
"MeasureTheory.OuterMeasure.instZero",
"instIsBotZeroClass",
"Set.subset_univ",
"Set.univ",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"MeasureTheory.OuterMeasure",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"L... | true |
RingHom.formallyEtale_algebraMap | Mathlib.RingTheory.Etale.Basic | [
"Eq.mpr",
"CommRing",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"Algebra.FormallyEtale",
"Iff.rfl",
"Algebra",
"RingHom.FormallyEtale.eq_1",
"id",
"CommRing.toCommSemiring",
"Iff",
"RingHom.FormallyEtale",
"Eq",
"RingHom.toAlgebra",
"toAlgebra_algebraMap"
] | true |
Order.Ideal.coe_sup_eq | Mathlib.Order.Ideal | [
"Set.ext",
"Lattice.toSemilatticeSup",
"_private.Mathlib.Order.Ideal.0.Order.Ideal.coe_sup_eq.match_1_1",
"SemilatticeInf.instIsCodirectedOrder",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Order.Ideal.instMax",
"SemilatticeInf.toPartialOrder",
"Semilattic... | true |
CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_obj | Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.LaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory",
"CategoryTheory.PrelaxFunctorStruct.toPrefunctor",
"Eq.refl",
"Categor... | true |
SSet.splitting._proof_9 | Mathlib.AlgebraicTopology.SimplicialSet.Splitting | [
"Eq.mpr",
"Opposite",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SSet.exists_nonDegenerate",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Quiver.Hom.op",
"_private.Mathlib.AlgebraicTopology.SimplicialSet.Splitting.0.SSet.splitting.match_7",
"CategoryThe... | false |
ContinuousMultilinearMap.smulRight_apply | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"ContinuousMultilinearMap.smulRight",
"instHSMul",
"Semiring.toModule",
"ContinuousSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"ContinuousMultilinearMap",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"ContinuousMultilinearMap.funLik... | true |
Int.negOnePow_two_mul_add_one | Mathlib.Algebra.Ring.NegOnePow | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Units.instNeg",
"Units",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",
"Odd._proof_1",
"Int",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Int.negOnePow_odd... | true |
Std.Time.FormatPart.noConfusionType | Std.Time.Format.Basic | [
"Std.Time.FormatPart",
"String",
"Std.Time.FormatPart.casesOn",
"Std.Time.Modifier",
"Eq"
] | false |
Nat.testBit_ofBits_lt | Batteries.Data.Nat.Lemmas | [
"Nat.mul_add_mod_self_left",
"Eq.mpr",
"instNeZeroNatHAdd_1",
"False",
"Nat.recAux",
"Bool.toNat_lt",
"instHDiv",
"HMul.hMul",
"Fin.succ",
"congrArg",
"HEq.refl",
"Decidable.decide.congr_simp",
"False.elim",
"Nat.mul_add_div",
"Bool.toNat",
"noConfusion_of_Nat",
"Function.comp",
"N... | true |
Std.Do.Internal.MayReturn.mk._flat_ctor | Std.Do.Internal.Ensures.Def | [
"Std.Do.Internal.MayReturn.mk",
"Std.Do.Internal.Ensures",
"Std.Do.Internal.MayReturn",
"Bind"
] | false |
HahnSeries.leadingCoeff_abs | Mathlib.RingTheory.HahnSeries.Lex | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Preorder.toLT",
"Equiv.instEquivLike",
"abs",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Lex",
"Lex.instAddCommGroup",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"Partia... | true |
Lean.Parser.Term.doLetRec | Lean.Parser.Do | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"Lean.Parser.nonReservedSymbol",
"instHAndThenOfAndThen",
"Lean.Parser.group",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.Term.letRecDecls",
"Lean.Parser.withAntiquot",
"Bool.true",
"Unit",
"Nat",
"Lean.Parser.wi... | true |
isOpenMap_sigmaMk | Mathlib.Topology.Constructions | [
"Eq.mpr",
"congrArg",
"IsOpenMap",
"id",
"Ne",
"instTopologicalSpaceSigma",
"Or.casesOn",
"TopologicalSpace",
"Set.preimage_image_sigmaMk_of_ne",
"Set.preimage",
"propext",
"Set.instEmptyCollection",
"Eq.ndrec",
"eq_or_ne",
"Set.preimage_image_eq",
"Set.image",
"IsOpen",
"Or",
"S... | true |
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